Ensure all your ingredients have come to about room temperature.
Preheat the oven to 350°F and set a rack in the middle position. Grease a 9x9-inch baking tin (light-colored aluminum is best) and line with a sheet of parchment paper that just covers the bottom of the pan and hangs over the sides slightly. This will help you remove the cake from the tin.
In a small mixing bowl, whisk together the cornmeal, flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer with the beater attachment, or with a medium bowl and a hand mixer, beat the butter and sugar on medium speed until light and fluffy, about 2 minutes.
Add one egg at a time, mixing in between each addition until incorporated, ensuring to scrape down the bowl a few times. Mix in the honey.
Dump in the dry ingredients and mix on medium-low speed until about 75% combined.
With the mixer on low speed, pour in the buttermilk in a steady stream, then do the same with the oil. Turn the mixer off once the batter is smooth and all ingredients are totally incorporated.
Bake on the middle rack for 25 minutes, or until the top is deep golden brown and springs back in the middle when pressed gently.
Allow the cake to cool in the tin for about 5 minutes, then loosen the sides from the tin with a knife and lift it onto a wire rack to cool completely.
Once the cake has cooled, prepare the frosting. In a medium mixing bowl, beat together the cream cheese, powdered sugar, and salt until creamy and spreadable.
Spread swoops of the frosting onto the cake. Drizzle with about two tablespoons honey, smearing the honey into the frosting, if desired. Top with a sprinkle of flakey sea salt.